
- •Idmodel/norm
- •Xreginterprbf/cond
- •Xreginterprbf/condest
- •Vector instead of a matrix. That is, p is a row vector such that
- •Vector instead of a matrix. That is, p is a row vector such that
- •In place of 'vector' returns permutation matrices.
- •Eigenvalues and singular values
- •Values, sqrt(diag(c'*c)./diag(s'*s)).
- •If sigma is a real or complex scalar including 0, eigs finds the
- •Is symmetric or Hermitian, the form is tridiagonal.
- •Index appearing in the upper left corner.
- •In their order of appearance down the diagonal of aa-t*bb.
- •Matrix functions
- •Factorization utilities
- •Xreglinear/qrdelete
- •Is real) from Real Schur Form to Complex Schur Form. The Real
Factorization utilities
<qrdelete> - Delete a column or row from QR factorization.
QRDELETE Delete a column or row from QR factorization.
[Q1,R1] = QRDELETE(Q,R,J) returns the QR factorization of the matrix A1,
where A1 is A with the column A(:,J) removed and [Q,R] = QR(A) is the QR
factorization of A. Matrices Q and R can also be generated by
the "economy size" QR factorization [Q,R] = QR(A,0).
QRDELETE(Q,R,J,'col') is the same as QRDELETE(Q,R,J).
[Q1,R1] = QRDELETE(Q,R,J,'row') returns the QR factorization of the matrix
A1, where A1 is A with the row A(J,:) removed and [Q,R] = QR(A) is the QR
factorization of A.
Example:
A = magic(5); [Q,R] = qr(A);
j = 3;
[Q1,R1] = qrdelete(Q,R,j,'row');
returns a valid QR factorization, although possibly different from
A2 = A; A2(j,:) = [];
[Q2,R2] = qr(A2);
Class support for inputs Q,R:
float: double, single
See also qr, qrinsert, planerot.
Overloaded methods:
Xreglinear/qrdelete
Reference page in Help browser
doc qrdelete
<qrinsert> - Insert a column or row into QR factorization.
QRINSERT Insert a column or row into QR factorization.
[Q1,R1] = QRINSERT(Q,R,J,X) returns the QR factorization of the matrix A1,
where A1 is A=Q*R with an extra column, X, inserted before A(:,J). If A has
N columns and J = N+1, then X is inserted after the last column of A.
QRINSERT(Q,R,J,X,'col') is the same as QRINSERT(Q,R,J,X).
[Q1,R1] = QRINSERT(Q,R,J,X,'row') returns the QR factorization of the matrix
A1, where A1 is A=Q*R with an extra row, X, inserted before A(J,:).
Example:
A = magic(5); [Q,R] = qr(A);
j = 3; x = 1:5;
[Q1,R1] = qrinsert(Q,R,j,x,'row');
returns a valid QR factorization, although possibly different from
A2 = [A(1:j-1,:); x; A(j:end,:)];
[Q2,R2] = qr(A2);
Class support for inputs Q,R,X:
float: double, single
See also qr, qrdelete, planerot.
Reference page in Help browser
doc qrinsert
<rsf2csf> - Real block diagonal form to complex diagonal form.
RSF2CSF Real block diagonal form to complex diagonal form.
[U,T] = RSF2CSF(U,T) transforms the outputs of SCHUR(X) (where X
Is real) from Real Schur Form to Complex Schur Form. The Real
Schur Form has the real eigenvalues on the diagonal and the
complex eigenvalues in 2-by-2 blocks on the diagonal. The Complex
Schur Form is upper triangular with the eigenvalues of X on the
diagonal.
Arguments U and T represent the unitary and Schur forms of a
matrix A, such that A = U*T*U' and U'*U = eye(size(A)).
Class support for inputs U,T:
float: double, single
See also schur.
Reference page in Help browser
doc rsf2csf
<cdf2rdf> - Complex diagonal form to real block diagonal form.
CDF2RDF Complex diagonal form to real block diagonal form.
[V,D] = CDF2RDF(V,D) transforms the outputs of EIG(X) (where X is
real) from complex diagonal form to a real diagonal form. In
complex diagonal form, D has complex eigenvalues down the
diagonal. In real diagonal form, the complex eigenvalues are in
2-by-2 blocks on the diagonal. Complex conjugate eigenvalue pairs
are assumed to be next to one another.
Class support for inputs V,D:
float: double, single
See also eig, rsf2csf.
Reference page in Help browser
doc cdf2rdf
<balance> - Diagonal scaling to improve eigenvalue accuracy.
BALANCE Diagonal scaling to improve eigenvalue accuracy.
[T,B] = BALANCE(A) finds a similarity transformation T such
that B = T\A*T has, as nearly as possible, approximately equal
row and column norms. T is a permutation of a diagonal matrix
whose elements are integer powers of two so that the balancing
doesn't introduce any round-off error.
B = BALANCE(A) returns the balanced matrix B.
[S,P,B] = BALANCE(A) returns the scaling vector S and the
permutation vector P separately. The transformation T and
balanced matrix B are obtained from A,S,P by
T(:,P) = diag(S), B(P,P) = diag(1./S)*A*diag(S).
To scale A without permuting its rows and columns, use
the syntax BALANCE(A,'noperm').
See also eig.
Reference page in Help browser
doc balance
<planerot> - Givens plane rotation.
PLANEROT Givens plane rotation.
[G,Y] = PLANEROT(X), where X is a 2-component column vector,
returns a 2-by-2 orthogonal matrix G so that Y = G*X has Y(2) = 0.
Class support for input X:
float: double, single
See also qrinsert, qrdelete.
Reference page in Help browser
doc planerot
<cholupdate> - rank 1 update to Cholesky factorization.
CHOLUPDATE Rank 1 update to Cholesky factorization.
If R = CHOL(A) is the original Cholesky factorization of A, then
R1 = CHOLUPDATE(R,X) returns the upper triangular Cholesky factor of A + X*X',
where X is a column vector of appropriate length. CHOLUPDATE uses only the
diagonal and upper triangle of R. The lower triangle of R is ignored.
R1 = CHOLUPDATE(R,X,'+') is the same as R1 = CHOLUPDATE(R,X).
R1 = CHOLUPDATE(R,X,'-') returns the Cholesky factor of A - X*X'. An error
message reports when R is not a valid Cholesky factor or when the downdated
matrix is not positive definite and so does not have a Cholesky factorization.
[R1,p] = CHOLUPDATE(R,X,'-') will not return an error message. If p is 0
then R1 is the Cholesky factor of A - X*X'. If p is greater than 0, then
R1 is the Cholesky factor of the original A. If p is 1 then CHOLUPDATE failed
because the downdated matrix is not positive definite. If p is 2, CHOLUPDATE
failed because the upper triangle of R was not a valid Cholesky factor.
CHOLUPDATE works only for full matrices.
See also chol.
Reference page in Help browser
doc cholupdate
<qrupdate> - rank 1 update to QR factorization.
QRUPDATE Rank 1 update to QR factorization.
If [Q,R] = QR(A) is the original QR factorization of A, then
[Q1,R1] = QRUPDATE(Q,R,U,V) returns the QR factorization of A + U*V',
where U and V are column vectors of appropriate lengths.
QRUPDATE works only for full matrices.
See also qr, qrinsert, qrdelete.
Reference page in Help browser
doc qrupdate